Life and Death on an Infinite Grid

Chris PhanDepartment of MathematicsBucknell University

Abstract: In 1970, mathematician John H. Conway introduced his Game of Life, a simulation with very simple rules that nevertheless gives rise to rich, complicated behavior. In my talk, I will discuss some of the phenomenon seen in Conway's Game of Life, as well as some other types of cellular automata.

Frattini Extensions of Groups

Let G and H be groups. We say that G is a Frattini extension of H if there exists a normal subgroup N of G such that G/N ≅ H and N ≤ Φ(G). We'll discuss ways of constructing Frattini extensions of a given group H, paying particular attention to the case H ≅ PSL(2, F) where F is a locally finite infinite field.

Frattini Extensions of Groups

The Frattini subgroup Φ(G) of a group G is defined to be the intersection of all the maximal subgroups of G, with the understanding that Φ(G) = G if G has no maximal subgroups. We'll discuss some interesting questions about the Frattini subgroups of finitely generated groups: What groups H can occur as the Frattini subgroup of a finitely generated group? What can be said about a group K if K is isomorphic to a subgroup of Φ(G) for some finitely generated group G?

Student Panel: What I did with my summer vacation

Abstract: What will you do this summer? For some ideas on what is available and what some of Bucknell's mathematics students have done in the past, come to the student panel to hear students talk about their past summer experience. Students will speak about research experiences at Bucknell and other institutions, teaching experiences, and internships they received. A question and answer period will follow the session.

Statistics in Observational Astronomy

Katelyn AllersDepartment of Physics and AstronomyBucknell University

Abstract: Experiments in observational Astronomy have, by nature, conditions that are not well controlled. Observational Astronomers rely on the detection of photons to infer the properties of astronomical objects. Two things are detected as a part of the process: signal and noise, and knowing how to separate them lies at the heart of having a reliable data set. We will review the statistics used by astronomers when reducing photometric and spectroscopic data. With data in hand, a major goal of astronomers is to then infer the underlying physical properties of the objects under scrutiny. This is usually done by performing a statistical comparison to other data sets or theoretical models, and we will discuss the statistical tests commonly used for this purpose.

Gary GordonMathematics DepartmentLafayette College

Abstract: Suppose you have a die sitting on a table. Now you pick it up and roll it so that it occupies the same place on the table it did before. How many ways could you have done this so that none of the 6 numbers are in the same place? What if you have an n-dimensional die? We relate these questions to a famous hat-check problem from combinatorics, and interpret the answer in terms of a coat-check problem. Along the way, we'll meet derangements -- permutations with no fixed points. We will do some counting, some calculus, some geometry and some group theory. It is possible we may also have some fun.

A Mathematical Look at Approval Voting

Josh GarverDepartment of MathematicsBucknell University

Abstract: Approval voting systems allow voters to approve or disapprove of a number of candidates or options simultaneously, unlike majority voting where each voter is allowed to make at most one choice. We will look at some examples of societies defined by the idea of approval voting, and use mathematical concepts to examine when we can have agreement between voters in these societies. In doing so we will find some connections to pure mathematics including Hellys Theorem.

PIZZA and DRINKS provided. All are welcome.

Talk: Thursday, September 29, 12:00 noon in 268 Olin Science

Finding Mathematics in Poetry

JoAnne Growney

Guest poet-mathematician JoAnne Growney will lead a poetry reading (with occasional commentary) of poems with mathematical connections from the anthology Strange Attractors: Poems of Love and Mathematics (2008) and from her blog (Intersections -- Poetry with Mathematics). Contributions from audience members will be welcomed as time permits.

JoAnne Growney is co-editor of Strange Attractors: Poems of Love and Mathematics (A K Peters, 2008) and author of a chapbook of mathematical poems, My Dance is Mathematics (Paper Kite Press, 2006). Her 2010 collection, Red Has No Reason (Plain View Press), also contains a selection of poems with mathematical structure and imagery. Growney was a professor of mathematics at Bloomsburg University before moving to Maryland where her primary activity is poetry. She proselytizes for poetry-with-mathematics in her blog, http://poetrywithmathematics.blogspot.com.

The Goluptious Gamma Function

Karl VossDepartment of MathematicsBucknell University

Abstract: The gamma function dates from the first few decades after the invention of calculus. Euler is traditionally assigned credit for creating the gamma function and we will discuss what brought him to consider this remarkable function. The gamma function appears in a variety of different mathematical contexts. In particular, it can be used to solve an interesting problem related to the volume of the unit sphere.

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